In undergraduate calculus, the number pi is defined via the length of the circle, the length of the circle is defined as an inverse trigonometric function, and the value of pi is defined via pi

A blind spot in undergraduate mathematics: The circular definition of the length of the circle, and how it can be turned into an enlightening example

We highlight the fact that in undergraduate calculus, the number pi isdefined via the length of the circle, the length of the circle is defined as acertain value of an inverse trigonometric function, and this value is defined via pi, thus forming a circular definition, thus forming a circular definition.We present a way in which this error can be rectified and explain that this error is instructive and can beused as an enlightening topic for discussing different approaches tomathematics with undergraduate students.The number pi is defined via the length of the circle, the length of the circle is defined as acertain value of an inverse trigonometric function, and this value is defined via pi, thus forming a circular definition.We highlight the fact that in undergraduate calculus, the number pi isdefined via the length of the circle, the length of the circle is defined as acertain value of an inverse trigonometric function, and this value is defined via pi, thus forming a circular definition.We present a way in which this error can be rectified and explain that this error is instructive and can beused as an enlightening topic for discussing different approaches tomathematics with undergraduate students.